CN108267094B - Non-cylindrical surface interference splicing measurement system and method based on rotary CGH - Google Patents
Non-cylindrical surface interference splicing measurement system and method based on rotary CGH Download PDFInfo
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Abstract
The invention discloses a non-cylindrical surface interference splicing measurement system and method based on a rotary CGH (Carrier-grade height), wherein the system comprises a Fizeau planar interferometer, a CGH cylindrical wave converter, a non-cylindrical surface to be measured, a non-cylindrical surface adjusting device and a precise rotary table; the precision rotary table controls the CGH cylindrical wave converter to rotate so that the CGH cylindrical wave converter rotates around the central axis of the precision rotary table; the non-cylindrical surface to be measured is arranged on the non-cylindrical surface adjusting device; and the optical axis of the Fizeau planar interferometer is superposed with the optical axis of the CGH cylindrical wave converter, and the non-cylindrical surface adjusting device is adjusted to ensure that the best-fit cylindrical axis of the non-cylindrical surface to be measured is superposed with the focal axis of the cylindrical wavefront diffracted by the CGH cylindrical wave converter. In addition, the measuring method can obviously reduce the aberration of the off-axis sub-aperture of the non-cylindrical surface and accurately measure the surface shape error of the non-cylindrical optical element.
Description
Technical Field
The invention relates to the field of optical precision measurement, in particular to a non-cylindrical surface interference splicing measurement system and method based on rotary CGH.
Background
The cylindrical optical element (such as a cylindrical lens) can change the size of the imaging dimension in one dimension, for example, a point light spot can be converted into a line light spot, or the height of the image can be changed without changing the width of the image. This feature makes it indispensable in optical systems such as wavefront shaping, bar code scanning, light sheet illumination microscope, and line scanning microscope. In particular, cylindrical optical elements play a critical role in intense laser systems, synchrotron radiation devices, satellite guidance and navigation systems. The non-cylindrical surface (such as an elliptic cylinder, a parabolic cylinder and the like) introduces more parameters than the cylindrical surface during design, so that the non-cylindrical surface can correct aberration, improve image quality, simplify an optical system and reduce weight. Therefore, non-cylindrical optical elements are expected to gradually replace cylindrical lenses as key components in the optical systems described above. However, the precise detection of the surface shape error of the non-cylindrical optical element is a problem which is not solved in the field of optical measurement, and becomes a key factor which restricts the wide application of the non-cylindrical optical element.
At present, contact measurement methods, such as a three-coordinate measuring machine and a profiler, are mainly adopted for surface shape error detection of non-cylindrical optical elements. However, the contact measurement method has a low sampling rate, and it is difficult to obtain a high-resolution measurement result for representing the full-aperture surface shape error distribution of the non-cylindrical surface to be measured. In addition, the contact probe is easily worn, which may cause measurement errors and affect the final measurement result. The interferometric technique, as a branch of the optical three-dimensional measurement technique, has the characteristics of non-contact, full-field, high precision, high resolution and the like, so that the interferometric technique is increasingly widely applied in the fields of surface shape error detection of precision parts and optical elements and the like.
Because the error of the non-cylindrical surface deviating from the ideal cylindrical surface (also called non-cylindrical surface degree) is too large and far exceeds the vertical measurement range of the cylindrical surface interference system, the formed interference fringes are too dense to be analyzed. The compensator can convert the wave front emitted by the cylindrical surface interference system into the non-cylindrical surface wave front matched with the detected non-cylindrical surface, so that the purpose of interference detection is realized, but the compensator is designed aiming at the aberration balance of the surface to be detected, if the parameter of the surface to be detected slightly changes, the compensator can be redesigned, and huge waste of time and economic cost is caused. The interference splicing provides a new idea for solving the problems. The basic principle is that the object to be measured is divided into a plurality of small-sized sub-apertures, a local overlapping area is arranged between the adjacent sub-apertures, the local surface shape of the object to be measured is measured by using an interference system with a small aperture each time, all sub-aperture surface shape errors are measured by moving and rotating the object to be measured or the interference system, and then the full-aperture surface shape errors are obtained by using all sub-aperture measurement data by adopting a sub-aperture splicing method. The document "j.pen, h.xu, y.yu, and m.chen," sting assaying interference optics with large angular aperture alert, "meas.sci.technol., vol.26, No.2,25204, (2015)" follows the basic idea of interference splicing and obtains the full aperture profile error of the large numerical aperture cylindrical optical element. However, the use of subaperture stitching to detect non-cylindrical surfaces requires that the returned residual aberrations not exceed the vertical measurement range of the interferometric system in order to obtain a resolvable interferogram. To meet this requirement, the subaperture stitching method needs to shorten the width of the subaperture when detecting aspheric surfaces (or non-cylindrical surfaces) in order to reduce the residual aberrations returned. This will increase the number of sub-apertures needed for measurement, resulting in long measurement time, easy environmental interference, and low measurement accuracy.
In order to reduce the number of sub-apertures required for measurement and shorten the measurement time, a variable compensator can be added in the off-axis sub-aperture measurement process to compensate the deviation of the off-axis sub-aperture from the best-fit cylinder or sphere. However, unlike conventional null compensators, only the residual aberrations of the off-axis sub-aperture need to be reduced to within the vertical measurement range of the interferometer after compensation, in which case the compensator is referred to as a near-null compensator. Furthermore, because of the different aberrations that need to be compensated for in measuring the sub-apertures at different positions, a near-zero compensator is required that can produce aberrations of variable size.
The CN201210110946.4 patent document discloses a 'near-zero compensator, a surface shape measuring instrument and a measuring method for aspheric sub-aperture splicing measurement', the technical scheme provides that a pair of phase plates rotating in opposite directions are utilized to form a variable near-zero compensator, a phase function on each phase plate is formed by Zernike polynomials, two phase plates can generate variable coma and spherical aberration when rotating in opposite directions, partial aberration of sub-apertures at different positions on an aspheric surface can be compensated, and accordingly detection of a steepness aspheric surface by an interference splicing method is achieved. In addition, the document "m.tricard, a.kulawiec and m.bauer.sub.lateral arrangement interference of high-precision aspheres by integrating optical small.cirp apertures-Manufacturing Technology,2010,59(1), 547-; whereas astigmatism is introduced when the two wedge prisms are tilted as a whole with respect to the optical axis of the interferometer. By adjusting the two degrees of freedom, aberration with variable size can be generated, partial aberration compensation of sub-apertures at different positions on the aspheric surface is realized, and a resolvable interference pattern is obtained. However, the two methods need to additionally introduce a variable zero compensator in the detection optical path, which inevitably increases the measurement cost and increases the complexity of the optical path; in addition, the two methods are only suitable for rotationally symmetrical aspheric surfaces and are not suitable for interference detection of non-cylindrical surfaces.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings in the prior art and provide a non-cylindrical surface interference splicing measurement system based on a rotary CGH (Carrier grade height), which can realize surface shape error measurement of a high-gradient non-cylindrical optical element under the condition of not increasing a compensator and the number of sub-apertures required by measurement.
The invention also aims to apply the measuring method of the non-cylindrical surface interference splicing measuring system based on the rotary CGH.
In order to realize the purpose, the invention adopts the following technical scheme:
a non-cylindrical surface interference splicing measurement system based on a rotary CGH comprises a Fizeau plane interferometer, a CGH cylindrical surface wave converter, a non-cylindrical surface to be measured, a non-cylindrical surface adjusting device and a precise rotary table; the Fizeau planar interferometer is used for generating a plane wave; the CGH cylindrical wave converter is used for diffracting the plane wave into a cylindrical wave front, is arranged on the precision rotary table and is positioned between the Fizeau plane interferometer and the non-cylindrical surface to be detected; the precise rotary table is used for controlling the CGH cylindrical wave converter to rotate, so that the CGH cylindrical wave converter rotates around the central axis of the CGH cylindrical wave converter; the non-cylindrical surface to be measured is arranged on a non-cylindrical surface adjusting device, and the non-cylindrical surface adjusting device is a five-degree-of-freedom adjusting mechanism and is used for adjusting the spatial position of the non-cylindrical surface to be measured, and comprises three rotations and two linear motions; the optical axis of the Fizeau planar interferometer is superposed with the optical axis of the CGH cylindrical wave converter; and adjusting the non-cylindrical surface adjusting device to enable the best fitting cylindrical axis of the non-cylindrical surface to be measured to coincide with the focal axis of the cylindrical wavefront diffracted by the CGH cylindrical wave converter.
As a preferred technical scheme, the planar wave emitted by the fizeau planar interferometer forms a cylindrical wave front through the CGH cylindrical wave converter, enters the non-cylindrical surface to be measured, is reflected by the non-cylindrical surface to be measured, passes through the CGH cylindrical wave converter again, and finally returns to the interior of the fizeau planar interferometer to interfere with the reference light to form an interference pattern; wherein a non-cylindrical wavefront with variable size and shape is generated by changing the rotation angle of the CGH cylindrical wave converter.
As a preferred technical scheme, the measuring method of the non-cylindrical surface interference splicing measuring system based on the rotary CGH comprises the following steps:
s1), determining the F/number of the CGH cylindrical wave converter according to the theoretical surface profile of the non-cylindrical surface to be detected, and dividing the sub-aperture; f is the ratio of the back focal length to the aperture diameter of the CGH cylindrical wave converter;
s2), calculating the nominal motion amount of the sub-aperture according to the theoretical surface profile of the sub-aperture;
s3), adjusting the postures of the non-cylindrical surface to be detected and the CGH cylindrical wave converter according to the nominal motion amount of the sub-aperture to obtain a resolvable interference pattern;
s4), determining a nominal value of residual aberration according to the rotation quantity of the CGH cylindrical wave converter, thereby obtaining surface shape error data of the sub-aperture; the nominal value of the residual aberration is the aberration remained after the aberration generated by the rotary CGH cylindrical wave converter is subtracted from the theoretical surface profile; the surface shape error data is the deviation of an actual surface shape relative to a theoretical surface shape profile;
s5), splicing by a cylindrical splicing algorithm and a cylindrical surface interference splicing algorithm to obtain the full-aperture surface shape error of the non-cylindrical surface to be detected.
As a preferred technical solution, the specific process of step S1) is as follows:
firstly, the theoretical surface profile of the non-cylindrical surface to be measured is obtained by the design value provided by the lens manufacturer, and the specific calculation formula is as follows:
wherein Z represents the rise of the non-cylindrical surface to be measured; k represents a conic constant; y represents the horizontal coordinate perpendicular to the non-cylindrical surface axis, Y e [ -D/2, D/2]D represents the width of the clear aperture of the non-cylindrical lens to be measured; r represents the vertex curvature radius of the non-cylindrical surface; a. the4，A6，…，A14Representing the non-cylindrical surface coefficients;
secondly, calculating the radius R of the best fitting cylinder according to the theoretical surface profile of the non-cylindrical surface to be measuredbfc：
Wherein h represents the maximum value of the rise Z; then the non-cylindrical surface degree is obtained by the following formula:
the best fit cylinder is denoted CfThe non-cylindrical surface degree is the deviation between the non-cylindrical surface to be measured and the best fitting cylinder;
then, calculating the slope of the non-cylindrical surface degree, and determining the maximum value point and the minimum value point of the slope, wherein the maximum point is marked as A, and the minimum point is marked as B; determining a point in the AB interval, marking as M, and marking the corresponding surface shape between the point M and the point B as SMBSo that SMBThe deviation of the theoretical surface profile and the best fitting cylinder is in the dynamic measurement range of the Fizeau planar interferometer, and the best fitting cylinder is marked as CMB；
Finally, the best-fit cylinder C is determined by the length of MBMBDetermining the F/number of the CGH cylindrical wave converter according to the radius of the CGH cylindrical wave converter and the overlapping coefficient CoDividing the sub-aperture; the overlapping coefficient is the ratio of the overlapping area between adjacent sub-apertures to the area occupied by a single sub-aperture, and C is seto＝0.3。
As a preferred technical solution, step S2) is specifically: and calculating the optimal fitting cylinder by adopting a least square method according to the theoretical surface profile of the sub-aperture to obtain the axis position parameter of the optimal fitting cylinder, wherein the axis position parameter is also called as the nominal motion amount of the sub-aperture.
As a preferable technical solution, step S3) specifically includes: adjusting the non-cylindrical surface to be measured according to the nominal motion amount of the sub-aperture, so that one sub-aperture of the non-cylindrical surface to be measured enters the measurement visual angle of the Fizeau planar interferometer; then, the CGH cylindrical wave converter is adjusted to rotate around the central axis and change the rotation angle, so that coma with variable size is generated to compensate the aberration of the sub-aperture to be measured, the residual aberration returning to the inside of the interferometer is reduced, and a resolvable interferogram is obtained; and then, obtaining a measurement result by using a Fizeau planar interferometer, wherein the measurement result is a relative value and represents the deviation of the actual surface shape and the reference wavefront generated by the CGH cylindrical wave converter.
As a preferable technical solution, step S4) specifically includes: in order to obtain the surface shape error data of the sub-aperture, firstly, a nominal value of residual aberration is determined through digital measurement calculation according to the rotation quantity of the CGH cylindrical wave converter, and then the nominal value of the residual aberration is subtracted from a measurement result to obtain the surface shape error data of the sub-aperture; and finally, sequentially obtaining surface shape error data of other sub-apertures according to the nominal value of the residual aberration and the measurement result.
As a preferable technical solution, step S5) specifically includes:
firstly, surface shape error data of all sub-apertures are calculated according to the nominal motion amount of the sub-apertures
Transforming to a global three-dimensional coordinate system (x, y, z);
wherein R isbfcRadius of best-fit cylinder, R, representing subaperturebfRepresenting the back focal length of the CGH cylindrical wave transformer,
representing the surface shape error of the sub-aperture; x represents a coordinate along the non-cylindrical surface axis direction, and Y represents a horizontal coordinate perpendicular to the non-cylindrical surface axis direction;
then, three-dimensional surface shape error data of the sub-aperture is rough by adopting a cylindrical splicing algorithm, namely, the mutual position relation between the adjacent sub-apertures is determined by utilizing the deviation of the overlapped area in the radius direction, and the space coordinates of the adjacent sub-apertures are adjusted by adopting a rigid transformation method according to the result; subtracting the theoretical surface profile of the non-cylindrical surface to be measured from the result after the coarse registration to obtain the surface error of the sub-aperture;
and finally, accurately splicing the surface shape errors of all the sub-apertures by adopting a cylindrical surface interference splicing algorithm to obtain the full-aperture surface shape error of the non-cylindrical surface.
Compared with the prior art, the invention has the following advantages and effects:
(1) the system for measuring the surface shape error of the non-cylindrical optical element does not need to additionally add a compensator, and can generate the non-cylindrical surface wavefront with variable size by only rotating the CGH cylindrical wave converter, so as to compensate the residual aberration in the off-axis sub-aperture measurement result, thereby reducing the measurement cost.
(2) The system for measuring the surface shape error of the non-cylindrical optical element only needs one-dimensional rotation of the CGH, is easy to operate, and the mechanical precision of the adjusting mechanism is easier to guarantee.
(3) The measuring method provided by the invention can obviously reduce the aberration of the off-axis sub-aperture and obtain the resolvable interferogram, and when the existing method is used for measuring a non-cylindrical surface, the resolvable interferogram cannot be obtained due to too large deviation between the off-axis sub-aperture and the best fitting cylindrical surface.
Drawings
FIG. 1 is a schematic view of a measurement system of the present invention; wherein, the reference numbers: 1. a Fizeau planar interferometer; 2. a CGH cylindrical wave converter; 3. a non-cylindrical surface to be measured; 4. a non-cylindrical surface adjustment device; 5. provided is a precision turntable.
FIG. 2 is a schematic diagram of the implementation steps of the measurement method of the present invention.
3(a1) -3 (b3) are interferograms and phase maps acquired at off-axis sub-apertures simulated without a rotating CGH cylindrical wave converter in this embodiment; wherein fig. 3(a1), 3(a2), and 3(a3) are interferograms acquired at 3 off-axis sub-aperture positions, respectively; fig. 3(b1), 3(b2) and 3(b3) are phase maps obtained for the off-axis sub-aperture positions at 3, respectively.
4(a1) -4 (b3) are diagrams of interferograms and phase patterns acquired at off-axis sub-apertures for a rotating CGH cylindrical wave converter in this example; wherein fig. 4(a1), 4(a2), and 4(a3) are interferograms acquired at the same 3 off-axis sub-aperture position as before, respectively; fig. 4(b1), 4(b2) and 4(b3) are phase maps obtained at the same 3 off-axis sub-aperture positions as before, respectively.
Fig. 5 is a diagram illustrating a sub-aperture interferogram of the non-cylindrical surface to be measured according to an experiment in the present embodiment.
Fig. 6 is a diagram illustrating a sub-aperture surface shape error distribution of the non-cylindrical surface to be measured according to the experiment in this embodiment.
Fig. 7 is a diagram illustrating a full-aperture surface shape error distribution of the non-cylindrical surface to be measured in the present embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
As shown in fig. 1, a non-cylindrical surface interference splicing measurement system based on a rotary CGH comprises a fizeau plane interferometer 1, a CGH cylindrical wave converter 2, a non-cylindrical surface to be measured 3, a non-cylindrical surface adjusting device 4 and a precision turntable 5; the Fizeau planar interferometer 1 is used for generating a plane wave; the CGH cylindrical wave converter 2 is used for diffracting the plane wave into a cylindrical wave front; the CGH cylindrical wave converter 2 is arranged on a precision rotary table 5 and is positioned between the Fizeau planar interferometer 1 and the non-cylindrical surface 3 to be measured, and the precision rotary table 5 controls the CGH cylindrical wave converter 2 to rotate so that the CGH cylindrical wave converter 2 rotates around the central axis of the CGH cylindrical wave converter 2; the non-cylindrical surface 3 to be measured is arranged on a non-cylindrical surface adjusting device 4, and the non-cylindrical surface adjusting device 4 is a five-degree-of-freedom adjusting mechanism and is used for adjusting the spatial position of the non-cylindrical surface 3 to be measured, and comprises three rotations and two linear motions; the optical axis of the Fizeau planar interferometer 1 is superposed with the optical axis of the CGH cylindrical wave converter 2; adjusting the non-cylindrical surface adjusting device 4 to enable the best fitting cylindrical axis of the non-cylindrical surface 3 to be measured to coincide with the focal axis of the cylindrical wavefront diffracted by the CGH cylindrical wave converter 2; the axis of the best-fit cylinder refers to the axis of a reference non-cylinder closest to the non-cylindrical surface to be measured.
In this embodiment 1, a plane wave emitted by the fizeau plane interferometer 1 forms a cylindrical wavefront through the CGH cylindrical wave converter 2, the cylindrical wavefront is incident to the non-cylindrical surface 3 to be measured, the cylindrical wavefront is reflected by the non-cylindrical surface 3 to be measured, then the cylindrical wavefront passes through the CGH cylindrical wave converter 2 again, and finally the cylindrical wavefront returns to the interior of the fizeau plane interferometer 1 to interfere with the reference light to form an interference pattern; wherein by changing the rotation angle of the CGH cylindrical wave converter 2 a non-cylindrical wavefront is generated which is variable in size and shape.
Principle of the measurement system of this embodiment 1: firstly, adjusting the non-cylindrical surface to be measured according to the nominal motion amount of the sub-aperture measurement, so that the sub-aperture of the non-cylindrical surface to be measured enters the measurement visual angle of the interference system; secondly, rotating the CGH cylindrical wave converter to minimize residual aberration returned to the Fizeau plane interferometer after passing through the CGH cylindrical wave converter; then, according to the rotation amount of the non-cylindrical surface to be detected of the CGH, the aberration compensated after the CGH rotates is determined through digital measurement; then, the measurement of the surface shape error of the residual off-axis sub-aperture is completed according to the method; and finally, converting the subaperture surface shape error into global three-dimensional coordinate data, performing coarse registration by using a cylindrical splicing algorithm, and performing fine registration by using a cylindrical surface interference splicing algorithm to obtain the full-aperture surface shape error distribution of the non-cylindrical surface to be detected. The measurement system of the embodiment 1 does not need to additionally add a compensator, and only needs to rotate the CGH cylindrical wave converter, so that the residual aberration returning to the interferometer can be reduced, and the measurement cost can be reduced; the CGH cylindrical wave converter only needs to be rotated in one dimension, so that the operation is easy, and the mechanical precision of the adjusting table is easy to ensure.
Example 2
The following will describe in detail a measurement method of the non-cylindrical surface interference splicing measurement system based on the rotating CGH provided by the present invention.
As shown in fig. 2, a measuring method of a non-cylindrical surface interference splicing measuring system based on a rotating CGH includes the following steps:
s1), determining the F/number of the CGH cylindrical wave converter according to the theoretical surface profile of the non-cylindrical surface to be detected, and dividing the sub-aperture; the specific process is as follows:
firstly, the theoretical surface profile of the non-cylindrical surface to be measured is obtained by the design value provided by the lens manufacturer, and the specific calculation formula is as follows:
wherein Z representsMeasuring the rise of the non-cylindrical surface; k represents a conic constant; y represents the horizontal coordinate perpendicular to the non-cylindrical surface axis, Y e [ -D/2, D/2]D represents the width of the clear aperture of the non-cylindrical lens to be measured; r represents the vertex curvature radius of the non-cylindrical surface; a. the4，A6，…，A14Representing the non-cylindrical surface coefficients;
secondly, calculating the radius R of the best fitting cylinder according to the theoretical surface profile of the non-cylindrical surface to be measuredbfc：
Wherein, the maximum value of the rise Z is represented; then the non-cylindrical surface degree is obtained by the following formula:
the best fit cylinder is denoted CfThe non-cylindrical surface degree is the deviation between the non-cylindrical surface to be measured and the best fitting cylinder;
then, calculating the slope of the non-cylindrical surface degree, and determining the maximum value point and the minimum value point of the slope, wherein the maximum point is marked as A, and the minimum point is marked as B; determining a point in the AB interval, marking as M, and marking the corresponding surface shape between the point M and the point B as SMBSo that SMBThe deviation of the theoretical surface profile and the best fitting cylinder is in the dynamic measurement range of the Fizeau planar interferometer, and the best fitting cylinder is marked as CMB；
Finally, the best-fit cylinder C is determined by the length of MBMBDetermining the F/number of the CGH cylindrical wave converter according to the radius of the CGH cylindrical wave converter and the overlapping coefficient CoDividing sub-apertures, wherein F is the ratio of the back focal length to the aperture diameter of the CGH; the overlapping coefficient is the ratio of the overlapping area between adjacent sub-apertures to the area occupied by a single sub-aperture, and C is seto＝0.3。
S2), calculating the nominal motion amount of the sub-aperture according to the theoretical surface profile of the sub-aperture;
and calculating the optimal fitting cylinder by adopting a least square method according to the theoretical surface profile of the sub-aperture to obtain the axis position parameter of the optimal fitting cylinder, wherein the axis position parameter is also called as the nominal motion amount of the sub-aperture.
S3), adjusting the postures of the non-cylindrical surface to be detected and the CGH cylindrical wave converter according to the nominal motion amount of the sub-aperture to obtain a resolvable interference pattern;
adjusting the non-cylindrical surface to be measured according to the nominal motion amount of the sub-aperture, so that one sub-aperture of the non-cylindrical surface to be measured enters the measurement visual angle of the Fizeau planar interferometer; then, the CGH cylindrical wave converter is adjusted to rotate around the central axis and change the rotation angle, so that coma with variable size is generated to compensate the aberration of the sub-aperture to be measured, the residual aberration returned to the interior of the Fizeau planar interferometer is reduced, and a resolvable interference pattern is obtained; the measurement results are then obtained using a fizeau planar interferometer.
S4), determining a nominal value of residual aberration according to the rotation quantity of the CGH cylindrical wave converter, thereby obtaining surface shape error data of the sub-aperture;
the nominal value of the residual aberration refers to the residual aberration after the aberration generated by the rotary CGH cylindrical wave converter is subtracted from the theoretical surface profile; the surface shape error data refers to the deviation of an actual surface shape relative to a theoretical surface shape profile; in order to obtain the surface shape error data of the sub-aperture, firstly, a nominal value of residual aberration is determined through digital measurement calculation according to the rotation quantity of the CGH cylindrical wave converter, and then the nominal value of the residual aberration is subtracted from a measurement result to obtain the surface shape error data of the sub-aperture; and finally, sequentially obtaining surface shape error data of other sub-apertures according to the method.
S5), splicing by a cylindrical splicing algorithm and a cylindrical surface interference splicing algorithm to obtain a full-aperture surface shape error of the non-cylindrical surface to be detected; the specific process is as follows:
firstly, surface shape error data of all sub-apertures are calculated according to the nominal motion amount of the sub-apertures
Transforming to a global three-dimensional coordinate system (x, y, z);
wherein R isbfcRadius of best-fit cylinder, R, representing subaperturebfThe back focal length of the CGH is shown,
representing the surface shape error of the sub-aperture; x denotes the coordinate along the non-cylindrical surface axis direction and Y denotes the horizontal coordinate perpendicular to the non-cylindrical surface axis direction.
Then, three-dimensional surface shape error data of the sub-aperture is rough by adopting a cylindrical splicing algorithm, namely, the mutual position relation between the adjacent sub-apertures is determined by utilizing the deviation of the overlapped area in the radius direction, and the space coordinates of the adjacent sub-apertures are adjusted by adopting a rigid transformation method according to the result; subtracting the theoretical surface profile of the non-cylindrical surface to be measured from the result after the coarse registration to obtain the surface error of the sub-aperture;
and finally, accurately splicing the surface shape errors of all the sub-apertures by adopting a cylindrical surface interference splicing algorithm to obtain the full-aperture surface shape error of the non-cylindrical surface.
The following is a specific application example
The measured object is a plano-convex non-cylindrical lens, the vertex curvature radius is 13.984mm, the clear aperture is 20mm x 20mm, the conic constant k is 1, and the non-cylindrical coefficients are shown in table 1. According to the above non-cylindrical surface parameters, the method provided in this embodiment 2 is adopted to calculate and obtain the best-fit cylinder parameters of the off-axis sub-aperture, as shown in table 2. In order to compare with the existing interference splicing method, the CGH cylindrical wave converter is not rotated in the sub-aperture measuring process, the non-cylindrical surface to be measured is adjusted only according to the parameters given in the table 1, and then the interference measuring system is adopted to obtain the surface shape error data of each sub-aperture. Interference and phase patterns acquired at the off-axis sub-apertures were simulated as in fig. 3(a1) -fig. 3(b3) without the rotating CGH cylindrical wave converter. FIGS. 3(a1), 3(a2), and 3(a3) are interferograms acquired at 3 off-axis sub-aperture positions, respectively; fig. 3(b1), 3(b2) and 3(b3) are corresponding phase maps acquired at 3 off-axis sub-aperture positions, respectively; 4(a1) -4 (b3) are diagrams of interferograms and phase maps obtained at off-axis sub-apertures simulated by rotating the CGH cylindrical wave converter of this example 2; fig. 4(a1), 4(a2), and 4(a3) are interferograms acquired at the same 3 off-axis sub-aperture position as before, respectively; fig. 4(b1), 4(b2) and 4(b3) are phase maps obtained at the same 3 off-axis sub-aperture positions as before, respectively. Comparing the results of fig. 3(a1) -3 (b3) and 4(a1) -4 (b3), it can be seen that the measurement method provided in this embodiment 2 can significantly reduce the aberration of the off-axis sub-aperture and obtain resolvable interferograms, whereas when the non-cylindrical surface is measured by the conventional method, the resolvable interferograms cannot be obtained due to too large deviation between the theoretical profile of the off-axis sub-aperture and the best-fit cylindrical surface.
TABLE 1 coefficient of non-cylindrical surface
According to the parameters in table 2, the non-cylindrical lens is experimentally measured by using a splicing interference method, and as shown in fig. 5, a sub-aperture interferogram of the non-cylindrical lens to be measured is experimentally measured; FIG. 6 is a diagram of the error distribution of the sub-aperture surface shape of the non-cylindrical surface to be measured. FIG. 7 is a diagram of a full-aperture profile error profile of a non-cylindrical surface to be measured.
TABLE 2 best-fit Cylinder parameters for off-axis sub-Aperture
It is to be noted that, in embodiments 1 and 2, each included unit is merely divided according to functional logic, but is not limited to the above division as long as the corresponding function can be realized; in addition, specific names of the functional units are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present invention.
In addition, it can be understood by those skilled in the art that all or part of the steps in the above embodiments may be implemented by a program to instruct related hardware, and the corresponding program may be stored in a computer-readable storage medium, such as a ROM/RAM, a magnetic disk, or an optical disk.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (7)
1. A non-cylindrical surface interference splicing measurement system based on a rotary CGH is characterized by comprising a Fizeau plane interferometer (1), a CGH cylindrical surface wave converter (2), a non-cylindrical surface to be measured (3), a non-cylindrical surface adjusting device (4) and a precision rotary table (5); the Fizeau planar interferometer (1) is used for generating a plane wave; the CGH cylindrical wave converter (2) is used for diffracting plane waves into cylindrical wave fronts, and the CGH cylindrical wave converter (2) is installed on the precision rotary table (5) and is located between the Fizeau plane interferometer (1) and the non-cylindrical surface (3) to be detected; the precise rotary table (5) is used for controlling the CGH cylindrical wave converter (2) to rotate, so that the CGH cylindrical wave converter (2) rotates around the central axis of the precision rotary table; the non-cylindrical surface (3) to be measured is arranged on a non-cylindrical surface adjusting device (4), and the non-cylindrical surface adjusting device (4) is a five-degree-of-freedom adjusting mechanism and is used for adjusting the spatial position of the non-cylindrical surface (3) to be measured, and comprises three rotations and two linear motions; the optical axis of the Fizeau planar interferometer (1) is superposed with the optical axis of the CGH cylindrical wave converter (2); and adjusting the non-cylindrical surface adjusting device (4) to enable the best fitting cylindrical axis of the non-cylindrical surface (3) to be measured to coincide with the focal axis of the cylindrical wavefront diffracted by the CGH cylindrical wave converter (2).
2. The non-cylindrical surface interference splicing measurement system based on the rotary CGH (Carrier gas laser) according to claim 1, wherein the planar wave emitted by the Fizeau planar interferometer (1) forms a cylindrical surface wave through the CGH cylindrical wave converter (2), the cylindrical surface wave is incident to the non-cylindrical surface (3) to be measured, the cylindrical surface wave is reflected by the non-cylindrical surface (3) to be measured, then the cylindrical surface wave passes through the CGH cylindrical wave converter (2) again, and finally the cylindrical surface wave returns to the interior of the Fizeau planar interferometer (1) to interfere with the reference light to form an interference pattern; wherein a non-cylindrical wavefront with variable size and shape is generated by changing the rotation angle of the CGH cylindrical wave converter (2).
3. The measurement method of the rotating CGH based non-cylindrical surface interferometric splicing measurement system of any one of claims 1-2, comprising the steps of:
s1), determining the F/number of the CGH cylindrical wave converter according to the theoretical surface profile of the non-cylindrical surface to be detected, and dividing the sub-aperture; f is the ratio of the back focal length to the aperture diameter of the CGH cylindrical wave converter;
s2), calculating the nominal motion amount of the sub-aperture according to the theoretical surface profile of the sub-aperture, wherein the nominal motion amount of the sub-aperture is the axis position parameter of the best fitting cylinder obtained by adopting least square fitting according to the theoretical surface profile of the sub-aperture;
s3), adjusting the postures of the non-cylindrical surface to be detected and the CGH cylindrical wave converter according to the nominal motion amount of the sub-aperture to obtain a resolvable interference pattern;
s4), determining a nominal value of residual aberration according to the rotation quantity of the CGH cylindrical wave converter, thereby obtaining surface shape error data of the sub-aperture; the nominal value of the residual aberration is the aberration remained after the aberration generated by the rotary CGH cylindrical wave converter is subtracted from the theoretical surface profile; the surface shape error data is the deviation of an actual surface shape relative to a theoretical surface shape profile;
s5), splicing by a cylindrical splicing algorithm and a cylindrical surface interference splicing algorithm to obtain the full-aperture surface shape error of the non-cylindrical surface to be detected.
4. The measuring method of the non-cylindrical surface interference splicing measuring system based on the rotating CGH as claimed in claim 3, wherein the specific process of step S1) is as follows:
firstly, the theoretical surface profile of the non-cylindrical surface to be measured is obtained by the design value provided by the lens manufacturer, and the specific calculation formula is as follows:
wherein Z represents the rise of the non-cylindrical surface to be measured; k represents a conic constant; y represents the horizontal coordinate perpendicular to the non-cylindrical surface axis, Y e [ -D/2, D/2]D represents the width of the clear aperture of the non-cylindrical lens to be measured; r represents the vertex curvature radius of the non-cylindrical surface; a. the4，A6，…，A14Representing the non-cylindrical surface coefficients;
secondly, calculating the radius R of the best fitting cylinder according to the theoretical surface profile of the non-cylindrical surface to be measuredbfc：
Wherein h represents the maximum value of the rise Z; then the non-cylindrical surface degree is obtained by the following formula:
the degree of the non-cylindrical surface is marked as CfThe non-cylindrical surface degree is the deviation between the non-cylindrical surface to be measured and the best fitting cylinder;
then, calculating the slope of the non-cylindrical surface degree, and determining the maximum value point and the minimum value point of the slope, wherein the maximum point is marked as A, and the minimum point is marked as B; determining a point in the AB interval, marking as M, and marking the corresponding surface shape between the point M and the point B as SMBSo that SMBThe deviation of the theoretical surface profile and the best fitting cylinder is in the dynamic measurement range of the Fizeau planar interferometer, and the best fitting cylinder is marked as CMB；
Finally, the best-fit cylinder C is determined by the length of MBMBDetermining the F/number of the CGH cylindrical wave converter according to the radius of the CGH cylindrical wave converter and the overlapping coefficient CoDividing the sub-aperture; the overlapping coefficient is the ratio of the overlapping area between adjacent sub-apertures to the area occupied by a single sub-aperture, and C is seto＝0.3。
5. The measuring method of the non-cylindrical surface interference splicing measuring system based on the rotating CGH as claimed in claim 3, wherein the step S3) specifically comprises:
adjusting the non-cylindrical surface to be measured according to the nominal motion amount of the sub-aperture, so that one sub-aperture of the non-cylindrical surface to be measured enters the measurement visual angle of the Fizeau planar interferometer; then, the CGH cylindrical wave converter is adjusted to rotate around the central axis and change the rotation angle, so that coma with variable size is generated to compensate the aberration of the sub-aperture to be measured, the residual aberration returning to the inside of the interferometer is reduced, and a resolvable interferogram is obtained; and then, obtaining a measurement result by using a Fizeau planar interferometer, wherein the measurement result is a relative value and represents the deviation of the actual surface shape and the reference wavefront generated by the CGH cylindrical wave converter.
6. The measuring method of the non-cylindrical surface interference splicing measuring system based on the rotating CGH as claimed in claim 3, wherein the step S4) specifically comprises: in order to obtain the surface shape error data of the sub-aperture, firstly, a nominal value of residual aberration is determined through digital measurement calculation according to the rotation quantity of the CGH cylindrical wave converter, and then the nominal value of the residual aberration is subtracted from a measurement result to obtain the surface shape error data of the sub-aperture; and finally, sequentially obtaining surface shape error data of other sub-apertures according to the nominal value of the residual aberration and the measurement result.
7. The measuring method of the non-cylindrical surface interference splicing measuring system based on the rotating CGH as claimed in claim 3, wherein the step S5) specifically comprises:
firstly, surface shape error data of all sub-apertures are calculated according to the nominal motion amount of the sub-apertures
Transforming to a global three-dimensional coordinate system (x, y, z);
wherein R isbfcRadius of best-fit cylinder, R, representing subaperturebfRepresenting the CGH cylindrical waveThe back focal length of the transducer is such that,
representing the surface shape error of the sub-aperture; x represents a coordinate along the non-cylindrical surface axis direction, and Y represents a horizontal coordinate perpendicular to the non-cylindrical surface axis direction;
then, three-dimensional surface shape error data of the sub-aperture is rough by adopting a cylindrical splicing algorithm, namely, the mutual position relation between the adjacent sub-apertures is determined by utilizing the deviation of the overlapped area in the radius direction, and the space coordinates of the adjacent sub-apertures are adjusted by adopting a rigid transformation method according to the result; subtracting the theoretical surface profile of the non-cylindrical surface to be measured from the result after the coarse registration to obtain the surface error of the sub-aperture;
and finally, accurately splicing the surface shape errors of all the sub-apertures by adopting a cylindrical surface interference splicing algorithm to obtain the full-aperture surface shape error of the non-cylindrical surface.
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